Plane figure in the context of "Solid of revolution"

A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called vertices, are zero-dimensional points while the sides connecting them, also called edges, are one-dimensional line segments. A triangle has three internal angles, each one bounded by a pair of adjacent edges; the sum of angles of a triangle always equals a straight angle (180 degrees or π radians). The triangle is a plane figure and its interior is a planar region. Sometimes an arbitrary edge is chosen to be the base, in which case the opposite vertex is called the apex; the shortest segment between the base and apex is the height. The area of a triangle equals one-half the product of height and base length.

In Euclidean geometry, any two points determine a unique line segment situated within a unique straight line, and any three points that do not all lie on the same straight line determine a unique triangle situated within a unique flat plane. More generally, four points in three-dimensional Euclidean space determine a solid figure called tetrahedron.

Rotation, rotational or rotary motion is the movement of an object that leaves at least one point unchanged. In 2 dimensions, a plane figure can rotate in either a clockwise or counterclockwise sense around a point called the center of rotation. In 3 dimensions, a solid figure rotates around an imaginary line called an axis of rotation.

The special case of a rotation with an internal axis passing through the body's own center of mass is known as a spin (or autorotation). In that case, the surface intersection of the internal spin axis can be called a pole; for example, Earth's rotation defines the geographical poles. A rotation around an axis completely external to the moving body is called a revolution (or orbit), e.g. Earth's orbit around the Sun. The ends of the external axis of revolution can be called the orbital poles.

In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the mean position of all the points in the figure. The same definition extends to any object in ${\displaystyle n}$-dimensional Euclidean space.

In geometry, one often assumes uniform mass density, in which case the barycenter or center of mass coincides with the centroid. Informally, it can be understood as the point at which a cutout of the shape (with uniformly distributed mass) could be perfectly balanced on the tip of a pin.

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. Therefore, two distinct plane figures on a piece of paper are congruent if they can be cut out and then matched up completely. Turning the paper over is permitted.